A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field

Nasir Siddiqui, Fahim Yousaf, Fiza Murtaza, Muhammad Ehatisham-ul-Haq, M Usman Ashraf, Ahmed M Alghamdi and Ahmed S Alfakeeh

PLOS ONE, 2020, vol. 15, issue 11, 1-16

Abstract: Cryptography is commonly used to secure communication and data transmission over insecure networks through the use of cryptosystems. A cryptosystem is a set of cryptographic algorithms offering security facilities for maintaining more cover-ups. A substitution-box (S-box) is the lone component in a cryptosystem that gives rise to a nonlinear mapping between inputs and outputs, thus providing confusion in data. An S-box that possesses high nonlinearity and low linear and differential probability is considered cryptographically secure. In this study, a new technique is presented to construct cryptographically strong 8×8 S-boxes by applying an adjacency matrix on the Galois field GF(28). The adjacency matrix is obtained corresponding to the coset diagram for the action of modular group PSL(2,Z) on a projective line PL(F7) over a finite field F7. The strength of the proposed S-boxes is examined by common S-box tests, which validate their cryptographic strength. Moreover, we use the majority logic criterion to establish an image encryption application for the proposed S-boxes. The encryption results reveal the robustness and effectiveness of the proposed S-box design in image encryption applications.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0241890

DOI: 10.1371/journal.pone.0241890

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